From the ALSA wiki
A stream is a continuous sequence of frames that, when processed in realtime, produces audio.
Sound hardware, such as a sound card, may support multiple streams. Each "stream" is an audio source input, which is then mixed together for output. For example, you might play two mp3 files at the same time and hear them both on the output. Sound hardware which is capable of mixing streams must have an internal "mixer". Some older sound cards, before 1997, may not support multiple streams.